Is there any censorship board present for films and TV shows for Hollywood?

In the United States, there isn't a strict analogue for your Censor Board. Here, the First Amendment to the US Constitution provides protection to film makers, ensuring the government won't censor their work. However, the law doesn't prevent voluntary censorship, which is where the MPAA comes in. They're a trade group of movie studios who created a ratings system. Films can voluntarily be submitted to be rated by them.

Movie theaters in the US then do some enforcement of policies based on these ratings. For example, usually children under 17 are not allowed into rated R films unless accompanied by an adult. In addition, theaters will sometimes not screen any films that lack a rating. Theaters will also often refuse to screen NC-17 films, which ends up acting as a sort of censorship, as when a film is being made in part to make a profit, not being able to distribute it to thousands of theaters nationwide due to an NC-17 rating means the contents of the film will be self-censored down to rated R-levels of content.

Usually in the making of a film, a specific rating will be targeted for marketing reasons. So a film that the studio wants to have broad appeal will have its content crafted to ensure a PG-13 rating, which doesn't have the "no people under 17 can freely get in the theater" limitation that rated R films have. This helps ensure more people can easily watch the film in theaters.

And to answer your second question, the MPAA doesn't explain their criteria. A lot of directors guess at what is acceptable, and will even throw in some obvious, over the top scenes in hopes that something else (what they really want) will pass through. See "Censor Decoy" and "Getting Crap Past the Radar" on tvtrope.org's page.

Films have been covered. What is allowed to be aired on TV and radio is governed differently.

The Federal Communications Commission [FCC] governs broadcasts. Broadcasts are things like TV and radio which broadcast over the airwaves, but not cable and Internet. The FCC derives its authority from the idea that the bandwidth of the electromagnetic spectrum is limited and there can be a limited number of stations in a given area. Somebody has to step in to prevent a shouting match. The Federal government owns the airwaves and licenses their use via the FCC.

The FCC disallows "indecent programming or profane language" between 6am and 10pm, this is to avoid exposing children. "Obscene" broadcasts are disallowed at all times. The FCC derives this power from the logic that TV and radio are a community resource and thus should be used to "community standards".

The FCC publishes some guidelines about what is "indecent", "profane" and "obscene", and the courts have made many rulings, but in the end it's difficult to predict what the FCC will find a problem with, "community standards" change, and as a Federal agency they are somewhat subject to the whims of the current administration. They tend to disallow sex, nudity and harsh language but allow violence.

Eric Idle famously wrote The FCC Song in response to being fined $5000 for saying fuck once on the radio. Bono got away with saying fuck on the technicality that it wasn't referring to sex, similar how "ass" has been allowed. However, a half second of nipple at the Super Bowl half time show caused an enormous controversy and shake up of regulations.